Question: Is one allowed to daven be4 Netz in order to help the family (help with children, etc.)

Answer:

One may daven shacharis before sunrise under extenuating circumstances, and Reb Moshe Feinstein zatzal writes that one who needs to leave early to work is included. Presumably helping with the family is no less important. Reb Elyashiv shlita says that it is better to daven before netz with a minyan than to daven later without.